Nonparametric Euler Equation Identification and Estimation

We consider nonparametric identification and estimation of consumption based asset pricing Euler equations. This entails estimation of pricing kernels or equivalently marginal utility functions up to scale. The standard way of writing these Euler pricing equations yields Fredholm integral equations of the first kind, resulting in the ill posed inverse problem. We show that these equations can be written in a form that equals, (or with habits, resembles) Fredholm integral equations of the second kind, having well posed rather than ill posed inverses. We allow durables, habits, or both to affect utility. We show how to extend the usual method of solving Fredholm integral equations of the second kind to allow for the presence of habits. Using these results, we show with few low level assumptions that marginal utility functions and pricing kernels are locally nonparametrically identified, and we give conditions for finite set and point identification of these functions. Unlike the case of ill posed inverse problems, the limiting distribution theory for our nonparametric estimators should be relatively standard.